Problem: $A$ $B$ $C$ If: $ BC = 5x + 6$, $ AC = 67$, and $ AB = 6x + 6$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {6x + 6} + {5x + 6} = {67}$ Combine like terms: $ 11x + 12 = {67}$ Subtract $12$ from both sides: $ 11x = 55$ Divide both sides by $11$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 5({5}) + 6$ Simplify: $ {BC = 25 + 6}$ Simplify to find ${BC}$ : $ {BC = 31}$